The government said Friday the economy created 151,000 nonfarm jobs last month, well short of the expected 180,000. The unemployment rate held steady at 4.9 percent, while average hourly earnings gained 0.1 percent.

Over the past three months, job gains have averaged 232,000.

Paulsen said the Fed should not look at just the August number, and instead put more emphasis on the strong moving average.

But even if the Fed were to hike rates, stock investors should be OK, he said. "Right now, we have a very strong correlation in the last six months between the 2-year [Treasury bond yield] movements and the stock market."

"If the Fed were raise rates in September it would be the first time maybe ever that the Fed would raise rates with a positive correlation," he added. "They could raise rates and the stock market should go up."

Paulsen also said an increase would send a signal to the market that the Fed thinks the economy is doing well.

Dan Suzuki, senior strategist at Bank of America Merrill Lynch, also warned on CNBC that investors not to read too much into the August job numbers to try to figure out the Fed. But he said a leading indicator in the report, the average workweek, was negative.

In an earlier "Squawk Box" interview, Diane Swonk, founder and CEO of DS Economics, saw the smaller-than-expected increase in average hourly earnings as a reason for the Fed wait to hike interest rates until December.

Wells Fargo Securities Chief Economist John Silvia said the Fed needs to act soon, arguing a hike in September or December would be fine. "The gate is wide open" and the Fed needs to "drive the truck through," he said.

Trump Economic Advisor Peter Navarro cited softness in manufacturing and construction jobs as a reason the Fed would stand pat. Navarro is an economics professor at the University of California, Irvine.

Austan Goolsbee, former Obama Council of Economic Advisers chairman, said the solid but weaker-than-expected nonfarm payrolls number did not make the case to hike rates before the November election.

The last time the Fed increased interest rates was in December. It was the Fed's first rate hike time in nearly a decade. At the time, policymakers had expected four additional rate hikes this year.